Question

Differentiate x^x with respect to x

Answer 1

Answer:

(i) Let y=x^x, and take logarithms of both sides of this equation: ln(y)=ln(x^x). Using properties of logarithmic functions, we can rewrite this as ln(y)=x. ln(x). Then differentiating both sides with respect to x, and using the chain rule on the LHS and product rule on the RHS gives 1/y.

Answer 2

Answer:

) Let y=x^x, and take logarithms of both sides of this equation: ln(y)=ln(x^x). Using properties of logarithmic functions, we can rewrite this as ln(y)=x. ln(x). Then differentiating both sides with respect to x, and using the chain rule on the LHS and product rule on the RHS gives 1/y.